document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208037>Question 1208037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You deposit $400 each month into an account earning 8% interest compounded monthly.<BR>\n" );
document.write( "a) How much will you have in the account in 15 years?<BR>\n" );
document.write( "b) How much total money will you put into the account?<BR>\n" );
document.write( "c) How much total interest will you earn?<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "(a) <font color=red>$138,415.29</font><BR>\n" );
document.write( "(b) <font color=red>$72,000</font><BR>\n" );
document.write( "(c) <font color=red>$66,415.29</font>\r<BR>\n" );
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document.write( "Explanation for part (a)\r<BR>\n" );
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document.write( "If we had one deposit, then we'd use the compound interest formula.<BR>\n" );
document.write( "However, we instead have a steady stream of deposits.<BR>\n" );
document.write( "So we must use the future value of annuity formula.\r<BR>\n" );
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document.write( "That particular formula is<BR>\n" );
document.write( "FV = P*( (1+i)^n - 1 )/i<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "FV = future value = account balance at some point in the future<BR>\n" );
document.write( "P = deposit amount per month<BR>\n" );
document.write( "i = interest rate per month in decimal form<BR>\n" );
document.write( "n = number of months\r<BR>\n" );
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document.write( "For this particular problem we have the following inputs<BR>\n" );
document.write( "P = 400 <BR>\n" );
document.write( "i = r/12 = 0.08/12, which I'll leave as a fraction<BR>\n" );
document.write( "n = 12*15 = 180 months (equivalent to 15 years)\r<BR>\n" );
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document.write( "Let's find the future value.<BR>\n" );
document.write( "FV = P*( (1+i)^n - 1 )/i<BR>\n" );
document.write( "FV = 400*( (1+0.08/12)^180 - 1 )/(0.08/12)<BR>\n" );
document.write( "FV = 138415.2886446 approximately<BR>\n" );
document.write( "FV = <font color=red>138415.29</font>\r<BR>\n" );
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document.write( "Explanation for part (b)\r<BR>\n" );
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document.write( "P = 400 dollars deposited each month.<BR>\n" );
document.write( "n = 180 months<BR>\n" );
document.write( "n*P = 180*400 = <font color=red>72000</font> dollars is the total amount you deposit over the 15 year timespan.\r<BR>\n" );
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document.write( "Explanation for part (c)\r<BR>\n" );
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document.write( "To find the amount of total interest, subtract the previous results.<BR>\n" );
document.write( "interest = (result of part A) - (result of part B)<BR>\n" );
document.write( "interest = 138415.29 - 72000<BR>\n" );
document.write( "interest = <font color=red>66415.29</font><BR>\n" );
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